The over 60 years old Rashba-Dresselhaus effect predicts spin-orbit coupling (SOC) induced momentum-dependent spin splitting and spin polarization in materials with noncentrosymmetric structures. Strong SOC induced effects usually require high-atomic number (Z) elements such as rare-earth elements. It has recently been pointed out [Yuan et al., Phys. Rev. B 102, 014422 (2020)] that antiferromagnets could hold SOC-independent spin splitting and spin polarization. In the present work we develop the spatial and magnetic symmetry conditions enabling such antiferromagnet (AFM)-induced spin splitting, dividing the 1651 magnetic space groups into seven different spin splitting prototypes (SST-1 to SST-7). This analysis places the physics of AFM spin splitting (SST-4) within the broader context of symmetry conditions that enable the more familiar forms of spin splitting, such as ferromagnetic Zeeman effect (SST-5), nonmagnetic no spin splitting (SST-6), and the nonmagnetic Rashba and Dresselhaus effects (SST-7). The AFM-induced spin splitting and spin polarization do not necessarily require breaking of inversion symmetry or the presence of SOC, hence can exist even in centrosymmetric, low-Z light element compounds, considerably broadening the material base for spin manipulations. We use the “inverse design” approach of first formulating the target property (here, spin splitting in low-Z compounds not restricted to low symmetry structures), then derive the enabling physical design principles—the magnetic symmetry conditions—to search realizable compounds that satisfy these a priori design principles. This process uncovers 422 magnetic space groups (160 centrosymmetric and 262 noncentrosymmetric) that could hold AFM-induced, SOC-independent spin splitting and spin polarization. We then search for stable compounds following such enabling symmetries. We investigate the electronic and spin structures of some selected prototype compounds by density functional theory (DFT) and find spin textures that are different than the traditional Rashba-Dresselhaus patterns and exist even in the absence of SOC effect. We provide the DFT results for all antiferromagnetic spin splitting prototypes (SST-1, SST-2, SST-3, SST-4), and concentrate on two limits of SST-4 that are particularly unusual: When spin splitting is momentum dependent (just like the Rashba effect) but is enabled in antiferromagnets even in the absence of SOC in the Hamiltonian. This includes examples of (a) centrosymmetric SST-4A compounds (e.g., orthorhombic $\mathrm{LaMn}{\mathrm{O}}_3$ illustrating collinear AFM, as well as cubic $\mathrm{Ni}{\mathrm{S}}_2$ illustrating noncollinear AFM) and (b) noncentrosymmetric SST-4B compounds (e.g., rhombohedral $\mathrm{MnTi}{\mathrm{O}}_3$ illustrating collinear AFM and hexagonal $\mathrm{ScMn}{\mathrm{O}}_3$ illustrating noncollinear AFM). The symmetry design principles outlined here, along with their transformation into an inverse design material search approach and DFT verification, could open the way to their experimental examination.

Correlated materials with open-shell $d$ and $f$ ions having degenerate band-edge states show a rich variety of interesting properties ranging from metal-insulator transition to unconventional superconductivity. The textbook view for the electronic structure of these materials is that mean-field approaches are inappropriate, as the interelectronic interaction U is required to open a band gap between the occupied and unoccupied degenerate states while retaining symmetry. We show that the latter scenario often defining what Mott insulators are is in fact not needed for the $3d$ binary oxides MnO, FeO, CoO, and NiO. The mean-field-like band theory can indeed lift such degeneracies in the binaries when nontrivial unit-cell representations (polymorphous networks) are allowed to break symmetries, in conjunction with a recently developed nonempirical exchange and correlation density functional without an on-site interelectronic interaction U. We explain how density-functional theory in the polymorphous representation achieves band-gap opening in correlated materials through a separate mechanism from the Mott-Hubbard approach. We show the method predicts magnetic moments and gaps for the four binary monoxides in both the antiferromagnetic and paramagnetic phases, offering an effective alternative to symmetry-conserving approaches for studying a range of functionalities in open $d$- and $f$-shell complex materials.

Traditional band theory of perfect crystalline solids often uses as input the structure deduced from diffraction experiments; when modeled by the minimal unit cell this often produces a spatially averaged model. The present study illustrates that this is not always a safe practice unless one examines if the intrinsic bonding mechanism is capable of benefiting from the formation of a distribution of lower symmetry local environments that differ from the macroscopically averaged structure. This can happen either due to positional or to magnetic symmetry breaking. By removing the constraint of a small crystallographic cell, the energy minimization in the density functional theory finds atomic and spin symmetry breaking, not evident in conventional diffraction experiments but being found by local probes such as atomic pair distribution function analysis. Here we report that large atomic and electronic anomalies in bulk tetragonal FeSe emerge from the existence of distributions of local positional and magnetic moment motifs. The found symmetry-broken motifs obtained by minimization of the internal energy represent what chemical bonding in the tetragonal phase prefers as intrinsic energy lowering (stabilizing) static distortions. This explains observations of band renormalization, predicts orbital order and enhanced nematicity, and provides unprecedented close agreement with spectral function measured by photoemission and local atomic environment revealed by the pair distribution function. While the symmetry-restricted strong correlation approach has been argued previously to be the exclusive theory needed for describing the main peculiarities of FeSe, we show here that the symmetry-broken mean-field approach addresses numerous aspects of the problem, provides intuitive insight into the electronic structure, and opens the door for large-scale mean-field calculations for similar $d$-electron quantum materials.

Garnet-type Li_6.5La₃Zr_1.5Ta_0.5O₁₂ (LLZO) is considered a promising solid electrolyte, but the surface degradation in air hinders its application for all-solid-state battery. Recent studies have mainly focused on the final products of the LLZO surface reactions due to lacking of powerful in situ characterization methods. Here, we use ambient pressure X-ray spectroscopies to in situ investigate the dynamical evolution of LLZO surface in different gas environments. The newly developed ambient pressure mapping of resonant Auger spectroscopy clearly distinguishes the lithium containing species, including LiOH, Li₂O, Li₂CO₃ and lattice oxygen. The reaction of CO₂ with LLZO to form Li₂CO₃ is found to be a thermodynamically favored self-limiting reaction. On the contrary, the reaction of H₂O with LLZO lags behind that of CO₂, but intensifies at high pressure. More interestingly, the results provide direct spectroscopic evidence for the existence of Li⁺/H⁺ exchange and reveal the importance of the initial layer formed on clean electrolyte surface in determining their air stability. This work demonstrates that the newly developed in situ technologies pave a new way to investigate the oxygen evolution and surface degradation mechanism in energy materials.

In some $d$-electron oxides, the measured effective mass $m_{\mathrm{exptl}}^{*}$ has long been known to be significantly larger than the model effective mass $m_{\mathrm{model}}^{*}$ deduced from mean-field band theory, i.e., $m_{\mathrm{exptl}}^{*}=\beta m_{\mathrm{model}}^{*}$, where $\beta >1$ is the “mass-enhancement” or “mass-renormalization” factor. Previous applications of density functional theory (DFT), based on a symmetry-restricted structure with the smallest number of possible magnetic, orbital, and structural degrees of freedom, missed such mass enhancement. This fact has been taken as evidence of strong electronic correlation, often described via the symmetry-restricted dynamic mean-field approach of the many-body theory, being the exclusive enabling physics. This paper uses instead a static density functional approach that does not restrict positional or spin degrees of freedom (symmetry-broken structures). This approach analyzes the contributions of different symmetry-broken modalities to mass enhancement for a few nominally highly correlated $d$-electron perovskites as well as the nominally uncorrelated, closed-shell $s\text{−}p$ bonding perovskites. It shows that the energy-lowering symmetry-broken spin effects (e.g., nonzero local moment in the paramagnetic phase) and structural effects (e.g., atomic displacement) as described in mean-field DFT already manifest mass enhancement for both electrons and holes in a range of $d$-electron perovskites $\mathrm{SrV}{\mathrm{O}}_3, \mathrm{SrTi}{\mathrm{O}}_3, \mathrm{BaTi}{\mathrm{O}}_3$, and $\mathrm{LaMn}{\mathrm{O}}_3$, as well as $p$-electron perovskites $\mathrm{CsPb}{\mathrm{I}}_3$ and $\mathrm{SrBi}{\mathrm{O}}_3$, including both metals ($\mathrm{SrV}{\mathrm{O}}_3$) and insulators (the rest). This is revealed only when enlarged unit cells of the same parent global symmetry, which are large enough to allow for symmetry-breaking distortions and concomitant variations in spin order, are explored for their ability to lower the total energy. Positional symmetry breaking that leads to mass enhancement includes octahedral rotation in halide perovskites such as $\mathrm{CsPb}{\mathrm{I}}_3$, Jahn-Teller-like $Q_2^{+}$ distortion in $\mathrm{LaMn}{\mathrm{O}}_3$, and bond disproportionation in $\mathrm{SrBi}{\mathrm{O}}_3$, while magnetic symmetry breaking resulting in mass enhancement includes the formation of a distribution of local moments in $\mathrm{SrV}{\mathrm{O}}_3$ that averages to zero in the paramagnetic phase. Not all symmetry breaking leads to significant mass enhancement, e.g., the rather small octahedral rotations in the nearly perfectly cubic $\mathrm{SrTi}{\mathrm{O}}_3$ cause negligible mass enhancement, as do the paraelectric displacements in $\mathrm{BaTi}{\mathrm{O}}_3$. In principle, by ergodicity, the two descriptions, i.e., the symmetry-restricted dynamic approach with a single time-fluctuating magnetic moment and the symmetry-broken mean-field approach with a static distribution of spatially fluctuated local moments, are not mutually exclusive but are a choice of representation and consequently, a choice of computational efficiency. In approximate implementations, the symmetry-broken mean-field approach appears to remove much of what was strong correlation in dynamically correlated symmetry-restricted solutions, leaving smaller (“weak”) residual correlation with respect to the exact solution.